Passages similar to: Secret Teachings of All Ages — Pythagorean Mathematics
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Secret Teachings of All Ages
Pythagorean Mathematics (75)
The one was defined by the Platonists as "the summit of the many." The one differs from the monad in that the term monad is used to designate the sum of the parts considered as a unit, whereas the one is the term applied to each of its integral parts.
For there is no single existing being, which does not participate in the one, but as every number participates in an unit, and one dual and one decade...
(2) But One, because He is uniquely all, as beseems an excess of unique Oneness, and is Cause of all without departing from the One. For there is no single existing being, which does not participate in the one, but as every number participates in an unit, and one dual and one decade is spoken of, and one half, and one third and tenth, so everything, and part of everything participates in the one, and by the fact that the One is, all existing things are. And the Cause of all is not One, as one of many, but before every one and multitude, and determinative of every one and multitude. For there is no multitude which does not partake in some way or other of the one. Yea, that which is many by parts, is one in the whole; and the many by the accidents, is one by the subject; and the many by the number or the powers, is one by the species, and the many by the species, is one by the genus; and the many by the progressions, is one by the source. And there is no single thing which does not participate in some way in the one, which uniformly pre-held in the uniqueness throughout all, all and whole, all, even the things opposed. And indeed, without the one there will not be a multitude, but without the multitude there will be the one, even as the unit previous to every multiplied number; and, if any one should suppose, that all things are united to all, the All will be one in the whole.
We may be told that unity and monad have no real existence, that the only unity is some definite object that is one thing, so that all comes to an...
(12) We may be told that unity and monad have no real existence, that the only unity is some definite object that is one thing, so that all comes to an attitude of the mind towards things considered singly.
But, to begin with, why at this should not the affirmation of Being pass equally as an attitude of mind so that Being too must disappear? No doubt Being strikes and stings and gives the impression of reality; but we find ourselves just as vividly struck and impressed in the presence of unity. Besides, is this attitude, this concept itself, a unity or a manifold? When we deny the unity of an object, clearly the unity mentioned is not supplied by the object, since we are saying it has none; the unity therefore is within ourselves, something latent in our minds independently of any concrete one thing.
"But the unity we thus possess comes by our acceptance of a certain idea or impression from things external; it is a notion derived from an object. Those that take the notion of numbers and of unity to be but one species of the notions held to be inherent in the mind must allow to numbers and to unity the reality they ascribe to any of the others, and upon occasion they must be met; but no such real existence can be posited when the concept is taken to be an attitude or notion rising in us as a by-product of the objects; this happens when we say "This," "What," and still more obviously in the affirmations "Crowd," "Festival," "Army," "Multiplicity." As multiplicity is nothing apart from certain constituent items and the festival nothing apart from the people gathered happily at the rites, so when we affirm unity we are not thinking of some Oneness self-standing, unrelated. And there are many other such cases; for instance "on the right," "Above" and their opposites; what is there of reality about this "On-the-right-ness" but the fact that two different positions are occupied? So with "Above": "Above" and "Below" are a mere matter of position and have no significance outside of this sphere.
Now in answer to this series of objections our first remark is that there does exist an actuality implicit in each one of the relations cited; though this is not the same for all or the same for correlatives or the same for every reference to unity.
That the Intellectual Beings Are Not Outside the Intellectual-principle: and on the Nature of the Good (5)
We return to our statement that The First remains intact even when other entities spring from it. In the case of numbers, the unit remains intact...
(5) We return to our statement that The First remains intact even when other entities spring from it.
In the case of numbers, the unit remains intact while something else produces, and thus number arises in dependence on the unit: much more then does the unit, The One, remain intact in the principle which is before all beings; especially since the entities produced in its likeness, while it thus remains intact, owe their existence to no other, but to its own all-sufficient power.
And just as there is, primarily or secondarily, some form or idea from the monad in each of the successive numbers- the later still participating, though unequally, in the unit- so the series of Beings following upon The First bear, each, some form or idea derived from that source. In Number the participation establishes Quantity; in the realm of Being, the trace of The One establishes reality: existence is a trace of The One- our word for entity may probably be connected with that for unity.
What we know as Being, the first sequent upon The One, advanced a little outward, so to speak, then chose to go no further, turned inward again and comes to rest and is now the reality and hearth of the universe. Pressing on the word for Being we have the word "hen" , an indication that in our very form of speech we tell, as far as may be, that Being is that which proceeds from The One. Thus both the thing that comes to be and Being itself are carriers of a copy, since they are outflows from the power of The primal One: this power sees and in its emotion tries to represent what it sees and breaks into speech "On"; "einai"; "ousia," "hestia" , sounds which labour to express the essential nature of the universe produced by the travail of the utterer and so to represent, as far as sounds may, the origin of reality.
In what sense, then, do we assert this Unity, and how is it to be adjusted to our mental processes? Its oneness must not be entitled to that of monad...
(6) In what sense, then, do we assert this Unity, and how is it to be adjusted to our mental processes?
Its oneness must not be entitled to that of monad and point: for these the mind abstracts extension and numerical quantity and rests upon the very minutest possible, ending no doubt in the partless but still in something that began as a partible and is always lodged in something other than itself. The Unity was never in any other and never belonged to the partible: nor is its impartibility that of extreme minuteness; on the contrary it is great beyond anything, great not in extension but in power, sizeless by its very greatness as even its immediate sequents are impartible not in mass but in might. We must therefore take the Unity as infinite not in measureless extension or numerable quantity but in fathomless depths of power.
Think of The One as Mind or as God, you think too meanly; use all the resources of understanding to conceive this Unity and, again, it is more authentically one than God, even though you reach for God's unity beyond the unity the most perfect you can conceive. For This is utterly a self-existent, with no concomitant whatever. This self-sufficing is the essence of its unity. Something there must be supremely adequate, autonomous, all-transcending, most utterly without need.
Any manifold, anything beneath The Unity, is dependent; combined from various constituents, its essential nature goes in need of unity; but unity cannot need itself; it stands unity accomplished. Again, a manifold depends upon all its factors; and furthermore each of those factors in turn- as necessarily inbound with the rest and not self-standing- sets up a similar need both to its associates and to the total so constituted.
The sovranly self-sufficing principle will be Unity-Absolute, for only in this Unity is there a nature above all need, whether within itself or in regard to the rest of things. Unity seeks nothing towards its being or its well-being or its safehold upon existence; cause to all, how can it acquire its character outside of itself or know any good outside? The good of its being can be no borrowing: This is The Good. Nor has it station; it needs no standing ground as if inadequate to its own sustaining; what calls for such underpropping is the soulless, some material mass that must be based or fall. This is base to all, cause of universal existence and of ordered station. All that demands place is in need; a First cannot go in need of its sequents: all need is effort towards a first principle; the First, principle to all, must be utterly without need. If the Unity be seeking, it must inevitably be seeking to be something other than itself; it is seeking its own destroyer. Whatever may be said to be in need of a good is needing a preserver; nothing can be a good to The Unity, therefore.
Neither can it have will to anything; it is a Beyond-Good, not even to itself a good but to such beings only as may be of quality to have part with it. Nor has it Intellection; that would comport diversity: nor Movement; it is prior to Movement as to Intellection.
To what could its Intellection be directed? To itself? But that would imply a previous ignorance; it would be dependent upon that Intellection in order to knowledge of itself; but it is the self-sufficing. Yet this absence of self-knowing does not comport ignorance; ignorance is of something outside- a knower ignorant of a knowable- but in the Solitary there is neither knowing nor anything unknown. Unity, self-present, it has no need of self-intellection: indeed this "self-presence" were better left out, the more surely to preserve the unity; we must eliminate all knowing and all association, all intellection whether internal or external. It is not to be though of as having but as being Intellection; Intellection does not itself perform the intellective act but is the cause of the act in something else, and cause is not to be identified with caused: most assuredly the cause of all is not a thing within that all.
This Principle is not, therefore, to be identified with the good of which it is the source; it is good in the unique mode of being The Good above all that is good.
The Origin and Order of the Beings. Following on the First (1)
The One is all things and no one of them; the source of all things is not all things; all things are its possession- running back, so to speak, to...
(1) The One is all things and no one of them; the source of all things is not all things; all things are its possession- running back, so to speak, to it- or, more correctly, not yet so, they will be.
But a universe from an unbroken unity, in which there appears no diversity, not even duality?
It is precisely because that is nothing within the One that all things are from it: in order that Being may be brought about, the source must be no Being but Being's generator, in what is to be thought of as the primal act of generation. Seeking nothing, possessing nothing, lacking nothing, the One is perfect and, in our metaphor, has overflowed, and its exuberance has produced the new: this product has turned again to its begetter and been filled and has become its contemplator and so an Intellectual-Principle.
That station towards the one establishes Being; that vision directed upon the One establishes the Intellectual-Principle; standing towards the One to the end of vision, it is simultaneously Intellectual-Principle and Being; and, attaining resemblance in virtue of this vision, it repeats the act of the One in pouring forth a vast power.
This second outflow is a Form or Idea representing the Divine Intellect as the Divine Intellect represented its own prior, The One.
This active power sprung from essence is Soul.
Soul arises as the idea and act of the motionless Intellectual-Principle- which itself sprang from its own motionless prior- but the soul's operation is not similarly motionless; its image is generated from its movement. It takes fulness by looking to its source; but it generates its image by adopting another, a downward, movement.
This image of Soul is Sense and Nature, the vegetal principle.
Nothing, however, is completely severed from its prior. Thus the human Soul appears to reach away as far down as to the vegetal order: in some sense it does, since the life of growing things is within its province; but it is not present entire; when it has reached the vegetal order it is there in the sense that having moved thus far downwards it produces- by its outgoing and its tendency towards the less good- another hypostasis or form of being just as its prior (the loftier phase of the Soul) is produced from the Intellectual-Principle which yet remains in untroubled self-possession.
The One is the circulation of the Light. If one begins, it is at first scattered and one tries to collect it; the six senses are not active. This is...
(10) The One is the circulation of the Light. If one begins, it is at first scattered and one tries to collect it; the six senses are not active. This is the care and nourishment of one's own origin, the illing up of the oil when one goes to receive life. When, one is far enough to have gathered it, one feels light and free and need take no further trouble. This is the quieting of the spirit in the space of the ancestors, the taking possession of former Heaven.
That the Intellectual Beings Are Not Outside the Intellectual-principle: and on the Nature of the Good (4)
We have said that all must be brought back to a unity: this must be an authentic unity, not belonging to the order in which multiplicity is unified...
(4) We have said that all must be brought back to a unity: this must be an authentic unity, not belonging to the order in which multiplicity is unified by participation in what is truly a One; we need a unity independent of participation, not a combination in which multiplicity holds an equal place: we have exhibited, also, the Intellectual Realm and the Intellectual-Principle as more closely a unity than the rest of things, so that there is nothing closer to The One. Yet even this is not The purely One.
This purely One, essentially a unity untouched by the multiple, this we now desire to penetrate if in any way we may.
Only by a leap can we reach to this One which is to be pure of all else, halting sharp in fear of slipping ever so little aside and impinging on the dual: for if we fail of the centre, we are in a duality which does not even include The authentic One but belongs on both sides, to the later order. The One does not bear to be numbered in with anything else, with a one or a two or any such quantity; it refuses to take number because it is measure and not the measured; it is no peer of other entities to be found among them; for thus, it and they alike would be included in some container and this would be its prior, the prior it cannot have. Not even essential number can belong to The One and certainly not the still later number applying to quantities; for essential number first appears as providing duration to the divine Intellection, while quantitative number is that which furnishes the Quantity found in conjunction with other things or which provides for Quantity independent of things, if this is to be thought of as number at all. The Principle which in objects having quantitative number looks to the unity from which they spring is a copy of the Principle which in the earlier order of number looks to the veritable One; and it attains its existence without in the least degree dissipating or shattering that prior unity: the dyad has come into being, but the precedent monad still stands; and this monad is quite distinct within the dyad from either of the two constituent unities, since there is nothing to make it one rather than the other: being neither, but simply that thing apart, it is present without being inherent.
But how are the two unities distinct and how is the dyad a unity, and is this unity the same as the unity by which each of the constituents is one thing?
Our answer must be that the unity is that of a participation in the primal unity with the participants remaining distinct from that in which they partake; the dyad, in so far as it is one thing, has this participation, but in a certain degree only; the unity of an army is not that of a single building; the dyad, as a thing of extension, is not strictly a unit either quantitatively or in manner of being.
Are we then to take it that the monads in the pentad and decad differ while the unity in the pentad is the same as that in the decad?
Yes, in the sense in which, big and little, ship is one with ship, army with army, city with city; otherwise, no. But certain difficulties in this matter will be dealt with later.
It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real...
(11) It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real existence why not the rest? We are certainly not compelled to attach that one henad to some one thing and so deprive all the rest of the means to unity: since every existent must be one thing, the unity is obviously common to all. This means one principle applying to many, the principle whose existence within itself we affirmed to be presupposed by its manifestation outside.
But if a henad exists in some given object and further is observed in something else, then that first henad being real, there cannot be only one henad in existence; there must be a multiplicity of henads.
Supposing that first henad alone to exist, it must obviously be lodged either in the thing of completest Being or at all events in the thing most completely a unity. If in the thing of completest Being, then the other henads are but nominal and cannot be ranked with the first henad, or else Number becomes a collection of unlike monads and there are differences among monads . If that first henad is to be taken as lodged in the thing of completest unity, there is the question why that most perfect unity should require the first henad to give it unity.
Since all this is impossible, then, before any particular can be thought of as a unit, there must exist a unity bare, unrelated by very essence. If in that realm also there must be a unity apart from anything that can be called one thing, why should there not exist another unity as well?
Each particular, considered in itself, would be a manifold of monads, totalling to a collective unity. If however Nature produces continuously- or rather has produced once for all- not halting at the first production but bringing a sort of continuous unity into being, then it produces the minor numbers by the sheer fact of setting an early limit to its advance: outgoing to a greater extent- not in the sense of moving from point to point but in its inner changes- it would produce the larger numbers; to each number so emerging it would attach the due quantities and the appropriate thing, knowing that without this adaptation to Number the thing could not exist or would be a stray, something outside, at once, of both Number and Reason.
The self-existent Super-goodness then, as projecting the first gift of self-existent being, is celebrated by the elder and first of the...
(6) The self-existent Super-goodness then, as projecting the first gift of self-existent being, is celebrated by the elder and first of the participations; and being itself is from It, and in It; as also the sources of things being, and all the things that be, and the things howsoever sustained by being, and that irresistibly, and comprehensively and uniformly. For even in a monad, every number preexists in the form of a unit, and the monad holds every number in itself singly. And every number is united in the monad, but so far as it advances from the monad, so far it is distributed and multiplied. And in a centre, all the lines of the circle coexist within one union, and the point holds all the straight lines in itself, uniformly united, both to each other, and to the one source from which they proceeded, and in the centre itself they are completely united; but standing slightly distant from it, they are slightly separated; but when more apart, more so. And in one word, the nearer they are to the centre, the more they are united to it and to each other? and the more they stand apart from it, the more they stand apart from each other.
We have to enquire into the existence of the Numbers in the Intellectual. Are they Ideas added to the other Ideas? Or are they no more than necessary...
(4) We have to enquire into the existence of the Numbers in the Intellectual. Are they Ideas added to the other Ideas? Or are they no more than necessary concomitants to the Ideas?
In the latter case, Being, as the first would give us the conception of the Monad; then since Being produces motion and rest, Three exists; and so on for all the other members of the realm of Being. Or perhaps there is one monad for each member, or a monad for the first, with a dyad for its next, since there exists a series, and a corresponding number for every successive total, decad for ten, and so on.
If, on the contrary, Number is a direct production of the Intellectual-Principle , there is the question whether it preceded or followed the other Ideas.
Plato, where he says that men arrived at the conception of Number by way of the changes of day and night- thus making the concept depend upon variation among things- seems to hold that the things numerable precede and by their differences produce number: Number then would consist in a process within the human mind passing onwards from thing to thing; it results by the fact that the mind takes count, that is when the mind traverses things and reports their differences; observing pure identity unbroken by difference, it says One. But there is the passage where he tells us that the veritable Number has Being, is a Being; this is the opposed view that Number is no product of the reckoning mind but a reality in itself, the concept of which is reawakened in the mind by changes in things of sense.
Chapter XII: God Cannot Be Embraced in Words or By the Mind. (9)
And therefore it is without form and name.
(9) For the One is indivisible; wherefore also it is infinite, not considered with reference to inscrutability, but with reference to its being without dimensions, and not having a limit. And therefore it is without form and name.
As I said earlier, among the things that were created the monad is first, the dyad follows it, and the triad, up to the tenths. Now the tenths rule...
(15) As I said earlier, among the things that were created the monad is first, the dyad follows it, and the triad, up to the tenths. Now the tenths rule the hundredths; the hundredths rule the thousandths; the thousands rule the ten thousands. This is the pattern immortals. First Man is like this: His monad [...].
I asked if I might understand this, and it said to me, The One is a sovereign that has nothing over it. It is god and father of all, the invisible...
I asked if I might understand this, and it said to me, The One is a sovereign that has nothing over it. It is god and father of all, the invisible one that is over all, that is incorruptible, that is pure light at which no eye can gaze. The One is the invisible spirit. We should not think of it as a god or like a god. For it is greater than a god, because it has nothing over it and no lord above it. It does not exist within anything inferior to it, since everything exists within it alone. It is eternal, since it does not need anything. For it is absolutely complete. It has never lacked anything in order to be completed by it. Rather, it is always absolutely complete in light. The One is illimitable, since there is nothing before it to limit it, unfathomable, since there is nothing before it to fathom it, immeasurable, since there was nothing before it to measure it, invisible, since nothing has seen it, eternal, since it exists eternally, unutterable, since nothing could comprehend it to utter it, unnamable, since there is nothing before it to give it a name. The One is the immeasurable light, pure, holy, immaculate. The One is unutterable and is perfect in incorruptibility. Not that it is part of perfection or blessedness or divinity: it is much greater. The One is not corporeal and is not incorporeal. The One is not large and is not small. It is impossible to say, “How much is it? What kind is it?” For no one can understand it. The One is not among the things that exist, but it is much greater. Not that it is greater. Rather, as it is in itself, it is not a part of the eternal realms or of time. For whatever is part of a realm was once prepared by another. Time was not allotted to it, since it receives nothing from anyone: what would be received would be on loan. The one who is first does not need to receive anything from another. Such a one beholds itself in its light. The One is majestic and has an immeasurable purity. The One is a realm that gives a realm, life that gives life, a blessed one that gives blessedness, knowledge that gives knowledge, a good one that gives goodness, mercy that gives mercy and redemption, grace that gives grace. Not as if the One possesses all this. Rather, it is that the One gives immeasurable and incomprehensible light. What shall I tell you about it? Its eternal realm is incorruptible, at peace, dwelling in silence, at rest, before everything. It is the head of all realms, and it sustains them through its goodness. We would not know what is ineffable, we would not understand what is immeasurable, were it not for what has come from the father. This is the one who has told these things to us alone.
How then can a multitude of essential beings be really one? Obviously either the one essence will be entire in all, or the many will rise from a one...
(5) How then can a multitude of essential beings be really one?
Obviously either the one essence will be entire in all, or the many will rise from a one which remains unaltered and yet includes the one- many in virtue of giving itself, without self-abandonment, to its own multiplication.
It is competent thus to give and remain, because while it penetrates all things it can never itself be sundered: this is an identity in variety.
There is no reason for dismissing this explanation: we may think of a science with its constituents standing as one total, the source of all those various elements: again, there is the seed, a whole, producing those new parts in which it comes to its division; each of the new growths is a whole while the whole remains undiminished: only the material element is under the mode of part, and all the multiplicity remains an entire identity still.
It may be objected that in the case of science the constituents are not each the whole.
But even in the science, while the constituent selected for handling to meet a particular need is present actually and takes the lead, still all the other constituents accompany it in a potential presence, so that the whole is in every part: only in this sense is the whole science distinguished from the part: all, we may say, is here simultaneously effected: each part is at your disposal as you choose to take it; the part invites the immediate interest, but its value consists in its approach to the whole.
The detail cannot be considered as something separate from the entire body of speculation: so treated it would have no technical or scientific value; it would be childish divagation. The one detail, when it is a matter of science, potentially includes all. Grasping one such constituent of his science, the expert deduces the rest by force of sequence.
the geometrician, in his analysis, shows that the single proposition includes all the items that go to constitute it and all the propositions which can be developed from it.
It is our feebleness that leads to doubt in these matters; the body obscures the truth, but There all stands out clear and separate.
The Great One is the term given to that which has nothing above it. The secret of the magic of life consists in using action in order to achieve...
(2) The Great One is the term given to that which has nothing above it. The secret of the magic of life consists in using action in order to achieve non-action. One must not wish to leave out the steps between and penetrate directlv. The maxim handed down to us is to take in hand the work on the essence. In doing this it is important not to follow the wrong road.
Especially must this be known, that according to the pre-conceived species of each one, things united are said to be made one, and the one is...
(3) Especially must this be known, that according to the pre-conceived species of each one, things united are said to be made one, and the one is elemental of all; and if you should take away the one, there will be neither totality nor part, nor any other single existing thing. For the one, uniformly, pre-held and comprehended all things in itself. For this reason, then, the Word of God celebrates the whole Godhead, as Cause of all, by the epithet of the One, both one God the Father, and one Lord Jesus Christ, and one and the same Spirit, by reason of the surpassing indivisibility of the whole Divine Oneness, in which all things are uniquely collected, and are super-unified, and are with It Superessentially. Wherefore also, all things are justly referred and attributed to It, by Which and from Which, and through Which, and in Which, and to Which, all things are, and are co-ordinated, and abide, and are held together, and are filled, and are turned towards It. And you would not find any existing thing, which is not what it is, and perfected and preserved, by the One, after which the whole Deity is superessentially named. And it is necessary also, that we being turned from the many to the One, by the power of the Divine Oneness, should celebrate as One the whole and one Deity--the one Cause of all--which is before every one and multitude, and part and whole, and limit and illimitability, and term and infinity, which bounds all things that be, even the Being Itself, and is uniquely Cause of all, individually and collectively, and at the same time before all, and above all, and above the One existing Itself, and bounding the One existing Itself; since the One existing--that in things being--is numbered, and number participates in essence; but the superessential One bounds both the One existing, and every number, and Itself is, of both one and number, and every being, Source and Cause, and Number and. Order. Wherefore also, whilst celebrated as Unit and Triad, the Deity above all is neither Unit nor Triad, as understood by us or by any other sort of being, but, in order that we may celebrate truly. Its super-oneness, and Divine generation, by the threefold and single name of God, we name the Deity, Which is inexpressible to things that be, the Superessential. But no Unit nor Triad, nor number nor unity, nor productiveness, nor any other existing thing, or thing known to any existing thing, brings forth the hiddenness, above every expression and every mind, of the Super-Deity Which is above all superessentially. Nor has It a Name, or expression, but is elevated above in the inaccessible. And neither do we apply the very Name of Goodness, as making it adequate to It, but through a desire of understanding and saying something concerning that inexpressible nature, we consecrate the most august of Names to It, in the first degree, and although we should be in accord in this matter with the theologians, yet we shall fall short of the truth of the facts. Wherefore, even they have given the preference to the ascent through negations, as lifting the soul out of things kindred to itself, and conducting it through all the Divine conceptions, above which towers that which is above every name, and every expression and knowledge, and at the furthest extremity attaching it to Him, as far indeed as is possible for us to be attached to that Being.
Anaxagoras, again, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in...
(9) Anaxagoras, again, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in precision.
Heraclitus, with his sense of bodily forms as things of ceaseless process and passage, knows the One as eternal and intellectual.
In Empedocles, similarly, we have a dividing principle, "Strife," set against "Friendship"- which is The One and is to him bodiless, while the elements represent Matter.
Later there is Aristotle; he begins by making the First transcendent and intellective but cancels that primacy by supposing it to have self-intellection. Further he affirms a multitude of other intellective beings- as many indeed as there are orbs in the heavens; one such principle as in- over to every orb- and thus his account of the Intellectual Realm differs from Plato's and, failing reason, he brings in necessity; though whatever reasons he had alleged there would always have been the objection that it would be more reasonable that all the spheres, as contributory to one system, should look to a unity, to the First.
We are obliged also to ask whether to Aristotle's mind all Intellectual Beings spring from one, and that one their First; or whether the Principles in the Intellectual are many.
If from one, then clearly the Intellectual system will be analogous to that of the universe of sense-sphere encircling sphere, with one, the outermost, dominating all- the First will envelop the entire scheme and will be an Intellectual Kosmos; and as in our universe the spheres are not empty but the first sphere is thick with stars and none without them, so, in the Intellectual Kosmos, those principles of Movement will envelop a multitude of Beings, and that world will be the realm of the greater reality.
If on the contrary each is a principle, then the effective powers become a matter of chance; under what compulsion are they to hold together and act with one mind towards that work of unity, the harmony of the entire heavenly system? Again what can make it necessary that the material bodies of the heavenly system be equal in number to the Intellectual moving principles, and how can these incorporeal Beings be numerically many when there is no Matter to serve as the basis of difference?
For these reasons the ancient philosophers that ranged themselves most closely to the school of Pythagoras and of his later followers and to that of Pherekudes, have insisted upon this Nature, some developing the subject in their writings while others treated of it merely in unwritten discourses, some no doubt ignoring it entirely.
When it takes lot with multiplicity, Being becomes Number by the fact of awakening to manifoldness;- before, it was a preparation, so to speak, of...
(10) When it takes lot with multiplicity, Being becomes Number by the fact of awakening to manifoldness;- before, it was a preparation, so to speak, of the Beings, their fore-promise, a total of henads offering a stay for what was to be based upon them.
Here with us a man will say "I wish I had such and such a quantity of gold"- or "such and such a number of houses." Gold is one thing: the wish is not to bring the numerical quantity into gold but to bring the gold to quantity; the quantity, already present in the mind, is to be passed on to the gold so that it acquire that numerical value.
If the Beings preceded the number and this were discerned upon them at the stirring, to such and such a total, of the numbering principle, then the actual number of the Beings would be a chance not a choice; since that total is not a matter of chance, Number is a causing principle preceding that determined total.
Number then pre-exists and is the cause by which produced things participate in quantity.
The single thing derives its unity by participation in Unity-Absolute; its being it derives from Being-Absolute, which holds its Being from itself alone; a unity is a unity in virtue of Being; the particular unity- where the unity is a multiple unity- is one thing only as the Triad is; the collective Being is a unity of this kind, the unity not of the monad but of the myriad or any such collective number.
Take a man affirming the presence of ten thousand things; it is he that produces the number; he does not tell us that the ten thousand have uttered it; they merely exhibit their several forms; the enumerator's mind supplies the total which would never be known if the mind kept still.
How does the mind pronounce?
By being able to enumerate; that is by knowing Number: but in order to this, Number must be in existence, and that that Principle should not know its own total content is absurd, impossible.
It is with Number as with Good. When we pronounce things to be good either we mean that they are in their own nature so or we affirm goodness as an accidental in them. Dealing with the primals, the goodness we have in mind is that First Hypostasis; where the goodness is an accidental we imply the existence of a Principle of Good as a necessary condition of the accidental presence; there must be some source of that good which is observed elsewhere, whether this source be an Absolute Good or something that of its own nature produces the good. Similarly with number; in attributing the decad to things we affirm either the truly existent decad or, where the decadhood is accidental, we necessarily posit the self-subsistent decad, decad not associated; if things are to be described as forming a decad, then either they must be of themselves the decad or be preceded by that which has no other being than that of decadhood.
It must be urged as a general truth that anything affirmed of a subject not itself either found its way in from outside or is the characteristic Act of that subject; and supposing the predicated attribute to show no variation of presence and absence but to be always present, then, if the subject is a Real Being so also is the accidental in an equal degree; or, failing Real Being, it at least belongs to the existents, it exists. In the case when the subject can be thought of as remaining without its Act, yet that Act is inbound with it even though to our minds it appears as a later; when on the contrary the subject cannot be conceived without the attribute-man, for example, without unity- then the attribute is either not later but concomitant or, being essential to the existence, is precedent. In our view, Unity and Number are precedent.